How about a gelatin glaze? Could even be chocolate flavoured gelatin. You could use it to lightly seal the inside and cold milk shouldn’t bother it. On the other hand, instead of baking the cups you could use actual choc chip cookies that you have crumbed and add gelatin to that mix and mould your cups in the fridge. It would take away the chrunchiness (add nuts?) and maybe make it more gummy - but it should seal and be edible.
